Two-stage model for multivariate longitudinal and survival data with application to nephrology research

In many follow-up studies different types of outcomes are collected including longitudinal measurements and time-to-event outcomes. Commonly, it is of interest to study the association between them. Joint modeling approaches of a single longitudinal outcome and survival process have recently gained increasing attention from both frequentist and Bayesian perspective. However, in many studies several longitudinal biomarkers are of interest and instead of selecting one single biomarker, the relationships between all these outcomes and their association with survival needs to be investigated. Our motivating study comes from Peritoneal Dialysis Programme in Nephrology research from Nephrology Unit, CHP (Hospital de Santo Antonio), Porto, Portugal in which the interest relies on the possible association between various biomarkers (calcium, phosphate, parathormone, and creatinine) and the patients' survival. To this aim, we propose a two-stage model-based approach for multivariate longitudinal and survival data that allowed us to study such complex association structure. The multivariate model suggested in this paper provided new insights in the area of nephrology research showing valid results in comparison with those models studying each longitudinal biomarker with survival separately.